Question

A metal surface is illuminated by photons of energy 5 eV and 2.5 eV respectively. The ratio of their wavelengths of emitted radiation is ______.

Options

• 1 : 4

• 1 : 2

• 2 : 1

• 4 : 1

Answer 1

A metal surface is illuminated by photons of energy 5 eV and 2.5 eV respectively. The ratio of their wavelengths of emitted radiation is 1 : 2.

Explanation:

The energy of a photon is given by:

E = `(hc)/lambda`

So, energy is inversely proportional to wavelength:

E ∝ `1/lambda`

Hence, the wavelength is inversely proportional to energy, so the ratio of wavelengths is the reverse of the ratio of energies.

∴ `lambda_1/lambda_2 = E_2/E_1`

`2.5/5 = 1/2`

∴ The ratio of their wavelengths is 1 : 2.